232 
Mr. Babbage’s essay towards 
From these ?z + 1 equations we may eliminate the n quan- 
tities •tyuXy -tycd x, and \| /& n x, and there will remain an equa- 
tion of the form 
F | a;, ccx, ccXy . . a n x, -tyx j == o 
from which -tyx may readily be found. 
Ex. 1. Let $x -f* ^ « x =fx and of x — x 
then -tyccx + =fax 
also \| jcdx~\- \px z=zfotx 
hence we find ipx = E (/# -—fax -\-fcd x ) 
Ex. s. take the equation 
$X -f -fx -tydX =fx 
I 
where/ and/ are perfectly arbitrary and cc oc - X 2 then making 
uee of process above described we find 
fx—fxfax 
S 2 
X — — l _j ax j ccx 
if a 3 x=x we should have 
fx —fx fax + fxfuxfa?x 
X 
X — fx fax fa . 2 X 
and generally when u n x = x we shall have 
fx — fx fax + fx fax fa? X — Sec. ±_fv fax . .fa 1 ' 2 X fa? \r 
*i» 'x 
X = — — — 
I —fx fax fa? X . . .fa 1 1 x 
Ex. 3. Take the equation 
•fyx \| >dX -\-fx ^x =Jx 
1 
if a?x=ct ?, must be deduced from the equation 
fx 
l 
f x 
fax 
fax + -4'.r 
